3.1 WARM-UP Graph each of the following problems 1. 4. 2. 5. 6. 3.

Solve Linear Systems by Graphing 3.1 Solve Linear Systems by Graphing A system of linear equations is 2 or more equations that intersect at the same point or have the same solution. You can find the solution to a system of equations in several ways. The one you are going to learn today is to find a solution by graphing. The solution is the ordered pair where the 2 lines intersect. In order to solve a system, you need to graph both equations on the same coordinate plane and then state the ordered pair where the lines intersect.

Consistent – a system that has at least one solution Classifying Systems Consistent – a system that has at least one solution Inconsistent – a system that has no solutions Independent – a system that has exactly one solution Dependent – a system that has infinitely many solutions Lines intersect at one point: consistent and independent Lines coincide; consistent and dependent Lines are parallel; inconsistent

GUIDED PRACTICE Graph each system and then estimate the solution. 4x – 5y = -10 2x – 7y = 4 3x + 2y = -4 x + 3y = 1 4x – 5y = -10 2x – 7y = 4 3x + 2y = -4 x + 3y = 1 -5y = -4x -10 -7y = -2x + 4 3y = -x + 1 2y = -3x - 4 From the graph, the lines appear to intersect at (–2, 1). From the graph, the lines appear to intersect at (–5, –2). Consistent & Independent Consistent & Independent

GUIDED PRACTICE 8x – y = 8 3x + 2y = -16 8x – y = 8 3x + 2y = -16 From the graph, the lines appear to intersect at (0, –8). Consistent & Independent

the system has no solution Solve the system. Then classify the system as consistent and independent,consistent and dependent, or inconsistent. 2x + y = 4 4x – 3y = 8 8x – 6y = 16 2x + y = 1 2x + y = 4 2x + y = 1 4x – 3y = 8 8x – 6y = 16 y = -2x + 1 y = -2x + 4 – 3y = -4x + 8 – 6y = -8x + 16 (the lines have the same slope) (the equations are exactly the same) the system has no solution inconsistent. consistent and dependent. The system has infinite solutions

Consistent and independent Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 2x + 5y = 6 4x + 10y = 12 2x + 5y = 6 4x + 10y = 12 A. Same equation Infinite solutions Consistent and independent 10y = -4x + 12 5y = -2x + 6 3x – 2y = 10 3x – 2y = 2 B. 3x – 2y = 10 3x – 2y = 2 Same slope // lines no solution inconsistent 2y = – 3x + 10 2y = – 3x + 2 (–1, 3) consistent independent C. – 2x + y = 5 y = – x + 2 – 2x + y = 5 y = – x + 2 y = 2x + 5

HOMEWORK 3.1 P.156 #3-10 and board work C. – 2x + y = 5 y = – x + 2 (–1, 3) consistent independent C. – 2x + y = 5 y = – x + 2 – 2x + y = 5 y = – x + 2 y = 2x + 5 Is (-1,3) the correct solution? – 2x + y = 5 y = – x + 2 3 = – (-1) + 2 – 2(-1) + (3)= 5 3 = 1 + 2 ☺ 2 + 3 = 5 ☺ HOMEWORK 3.1 P.156 #3-10 and board work

(3, 3) No solution (-1, 1) Infinite solutions

Consistent, independent 14. Solve each system of equations by graphing. Indicate whether the system is Consistent- Independent, Consistent-Dependent, or Inconsistent (-1, 3) Consistent, independent 5. no solution inconsistent, 6. 5. 6. 8. y = 3x - 2 Infinite solutions Consistent, dependent 7. (1, 2) Consistent, independent 8. 7. 9. y = x + 6 y = x + 5 No solutions Inconsistent 10. y= -x + 6 y = -x + 6 Infinite solutions Consistent, dependent 10. 9. 11. y = ½ x (2, 1) Consistent, independent 12. y = 1/2x + 4 Consistent, dependent Infinite solutions 12. 11. 13. y = -2x + 4 y = x - 2 (2, 0) Consistent, independent 14. y = -x + 2 y = -x + 6 No solutions inconsistent 14. 13. 15. y = -3x + 2 Consistent, dependent Infinite solutions 16. y = -2x + 4 y = 6x - 4 (1, 1) Consistent, independent 16. 15.